How do you simplify #7/(8sqrt7)#?
When working with fractions, we can think of pizza - the numerator tells us how many slices of pizza and the denominator tells us the size of the slices. When talking about the size of slices, having an irrational number defining the size of each slice is not helpful! And so we look to rationalize it.
In this case, we're working with a square root. We can rationalize the denominator by multiplying by the square root term: